Grid-Based and Hybrid Five-Step Block Runge-Kutta Methods for Solving Linear and Nonlinear First-Order Ordinary Differential Equations

Authors

  • Nafisat Orahano Adams Department of Mathematics, Federal University of Education Zaria, Kaduna State, Nigeria.
  • Ademola Mudshiru Badmus Department of Mathematical Sciences, Nigerian Defence Academy, Kaduna State Nigeria
  • Muhammed Yahuza Department of Mathematics, Federal University of Education Zaria, Kaduna State, Nigeria.

DOI:

https://doi.org/10.63561/jmns.v2i3.863

Keywords:

Grid Based, Hybrid, Block R K Method, linear and nonlinear

Abstract

The development of grid based and hybrid 5th Step Block Runge Kutta were constructed for the solution of both linear and non linear first order ordinary differential equations through interpolation and collocation approach. The 5th step Hybrid block Runge Kutta method converges faster with two problems tested.

References

Abualnaja, K. M. (2015). A Block Procedure with Linear Multi step Methods Using Legendre Polynomials for Solving Ordinary Differential Equations. Journal of Applied Mathematics, 6 (4), 717.

Kedir, A. K. (2021) ‘‘Numerical Solution of First Order Ordinary Differential Equation by Using Runge

Kutta Method. Journal of Systems Science and Applied Mathemaics, 6,(1), 1 8. doi: 10.11648/j.ijssam.20210601.11

Mshelia, D.W., Badmus, A.M., Yakubu, D.G., & Manjak, N.H. (2016). A Fifth Stage Runge Kutta method for the solution of ordinary differential equations. The Pacific Journal of Science and Technology, 17(2),87 100.

Ogunniran, M. O., Tayo, O. A., Haruna, Y., & Adebisi, A. F. (2020). Linear stability analysis of Runge Kutta methods for singular Lane Emden equations. Journal of the Nigerian Society of Physical Sciences. 2(3), 134 140. https://doi.org/10.46481/jnsps.2020.87

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Published

2025-05-30

How to Cite

Adams, N. O., Badmus, A. M., & Yahuza, M. (2025). Grid-Based and Hybrid Five-Step Block Runge-Kutta Methods for Solving Linear and Nonlinear First-Order Ordinary Differential Equations. Faculty of Natural and Applied Sciences Journal of Mathematical Modeling and Numerical Simulation, 2(3), 30–43. https://doi.org/10.63561/jmns.v2i3.863